Question

Find the area of pentagon ABCDE in which diagonal AD=10cm, the lengths of

perpendiculars are BP=4cm, CR=5cm, EQ=2cm, AP=2cm, AQ=4cm and AR=7cm.​

Answer 1

A=1

45(5+25)a2

d=1+5

2a

Solving forA

A=1

8d2(-5+45)20+5=1

8·102·(-5+45)·20+5≈65.71639cm²

Answer 2

Answer:

Area of pentagon ABCDE= Area of ΔABC+ Area of ΔACD+ Area of ΔADE

Here , BL⊥AC,CM⊥AD,EN⊥AD

So, BL, CM and EN perpendiculars to ΔABC,ΔACD and ΔADE respectively.

Area of triangle with perpendicular =1/2×base×height

∴ Area of ΔABC=1/2×AC×BL

Area of ΔACD=1/2×AD×CM

Area of ΔADE=1/2×AD×EN

Now area of pentagon ABCDE=1/2AC×BL+1/2×AD×CM+1/2×AD×EN

=(1/2×10×3)+(1/2×12×7)+(1/2×12×5)

=15+42+30

=87